(1) Field of the Invention
The invention relates to a multiplier circuit for multiplying an information signal x(t) by a periodic signal y(t), and which is particularly suitable for use in a stereo decoder or in a phase-locked loop (PLL).
(2) Description of the Prior Art
Circuits for multiplying signals are frequently used in, for example, amplitude modulators and amplitude demodulators. For the sake of simplicity, only the amplitude demodulator will be described hereinafter. The following is, however, also applicable to an amplitude modulator.
As is known, the object of an amplitude demodulator is to convert a band-limiter signal X(nf.sub.o ; t), whose frequency spectrum is located in a frequency band from (nf.sub.o -f.sub.1)Hz to (nf.sub.o +f.sub.1)Hz into a signal x(n,t), whose frequency spectrum is located in the frequency band from approximately 0 Hz to f.sub.1 Hz. The last-mentioned frequency band will be denoted AF-band (Audio Frequency band). In the foregoing, f.sub.o and also f.sub.1 is a fixed frequency and n is an integer. In practice X(nf.sub.o ; t) will be part of a signal x'(t) which in principle consists of an infinite number of band-limited signals. Consequently, this signal x'(t) might, for example, be mathematically represented as follows: ##EQU1## As usually only one of these band-limited signals must be converted to the AF-band (for example only the signal X(f.sub.o ; t) which is obtained if n=1), the amplitude modulator comprises a filter which is commonly referred to as a premodulation filter to which x'(t) is applied and which converts this signal into a signal x(t) which comprises only a limited number of these band-limited signals or even only the signal X(f.sub.o, t). Let it be assumed that for x(t) it holds that: ##EQU2## wherein N is, for example, equal to 8. Let it further be assumed that: EQU X(nf.sub.o ; t)=x(n;t) sin (2.pi.nf.sub.o t+.phi..sub.n) (3)
If now this signal x(t) is multiplied in the multiplier circuit by a periodic carrier signal y(t) having frequency f.sub.o for which it holds that, for example: EQU y(t)=2 sin (2.pi.f.sub.o t+.phi..sub.1) (4)
a product signal z(t) is obtained which in addition to the signal x(1;t) located in the AF-band further includes N-2 signals which are located around multiples of the frequency f.sub.o. By now applying the signal z(t) to a modulation filter which is commonly referred to as a post-modulation filter, those signals which are located around the multiples of the frequency f.sub.o can be suppressed, so that this filter supplies x(1;t) as the output signal.
If now the carrier signal y(t) would indeed vary purely sinusoidally and the multiplier circuit would operate purely linearly, then only the signal x(1;t) would indeed appear in the AF-band. However, in practice it has been found to be impossible to manufacture a purely linear amplifier circuit in a simple and cheap manner. It even appears to be impossible to generate a purely sinusoidally varying carrier signal in a simple manner. The result thereof is that in this demodulation procedure also noise signals are introduced in the AF-band, which may be particularly annoying.
In order to prevent these noise signals from occurring, it is at present general practice to use in storage decoders instead of a sinusoidally varying carrier signal a carrier signal which has the shape of a periodic two-level pulse signal having a pulse repetition rate f.sub.o and which may, for example, be mathematically expressed as: EQU y(t)=b1(2.pi.f.sub.o t+.phi.)=sign[sin (2.pi.f.sub.o t+.phi.)](5) ##EQU3## The output signal z(t) of this multiplier circuit is now defined by the relation: EQU z(t)=x(t)b1(2.pi.f.sub.o t+.phi.) (7)
For the two-level pulse signal defined in (5) there may now be written: ##EQU4## From this it follows that this two-level pulse signal comprises a signal component having a frequency which is equal to the pulse repetition rate f.sub.o. This signal component will be designated the basic component of the pulse signal. In addition to this basic component, this two-level pulse signal comprises signal components having frequencies which are a multiple, in this case an odd multiple, of the pulse repetition rate. Hereinafter such a signal component will be designated, for the sake of brevity, as "harmonic". In this connection, the expression "n.sup.th harmonic" then signifies a signal component whose frequency is equal to n times the frequency of the basic component.
If now the signal x(t) indicated in (2) is multiplied by the two-level pulse signal indicated in (8) then also the signals x(3;t), x(5;t), . . . will occur in the AF-band in addition to the signal x(1;t).
In order to prevent the signals x(3;t) from occurring in the AF-band, the corresponding signals X(3f.sub.o ;t) will have to be suppressed to a sufficient extent. The requirements then to be imposed on the premodulation filter appear to be so high in practice that only a filter which is hard to integrate and is costly can satisfy these requirements. To be able to alleviate these requirements, Reference 1 (see paragraph C) proposes to generate a carrier signal y(t) which has a frequency spectrum in which two harmonics of the basic component do not occur; for example the second and the third harmonics. To that end, no periodic two-level pulse signal is taken for y(t), but a periodic three-level signal in which there are three discrete amplitude levels; for example the levels +1, 0, -1. As y(t) does not comprise now the signal components having the frequencies 2f.sub.o and 3f.sub.o, the signals X(2f.sub.o ;t) and X(3f.sub.o ;t) are not converted to the AF-band. It is then not necessary for the premodulation filter to suppress these signals, so that, compared with the original filter, this filter may be of a simpler construction. In practice, such a three-level carrier signal is obtained by generating a first and a second two-level pulse signal which each have the pulse repetition rate f.sub.o. These two pulse signals can be chosen so that neither of them contains, for example, the second harmonic, but that both signals do contain the third harmonic. As follows, for example, from expression (8) these two two-level pulse signals can be shifted relative to each other so that the third harmonic in the first two-level pulse signal is accurately in anti-phase with the third harmonic in the second two-level pulse signal, so that these third harmonics cancel each other when these two two-level pulse signals are added together, whereby then the three-level signal is obtained at the same time. In a practical embodiment of this multiplier circuit there are to switching circuits, to which the signal x(t) is applied via their signal inputs. In addition, the first two-level pulse signal is applied to one of the switching circuits via a control input and the second two-level pulse signal to the other switching circuit. The signals supplied by the switching circuits are added together in an adder device. This method has the disadvantage that it produces a carrier signal y(t) which is indeed free from all even harmonics, but only one of the unwanted odd harmonics is absent. In a stereo decoder this will be the third harmonic of the 38 kHz subcarrier.
By means of the method proposed in Reference 1 it is possible to generate, starting from two two-level pulse signals, a so-called "multi-level" signal y(t) which is free from, for example, all the event harmonics, and one odd harmonic. A different method of generating, starting from two-level pulse signals, a multi-level signal y(t) which is free from one or more predetermined harmonics, amounts to the following. Starting from the assumption that y(t) must have a repetition rate f.sub.o, a first two-level pulse signal is generated having the pulse repetition rate f.sub.o and which does not contain the unwanted harmonics (let it, for example, be assumed that this pulse signal does not contain the even harmonics). If y(t) must now also be free from the odd n.sup.th harmonic (for example n=3), then a second two-level pulse signal is generated, whose pulse repetition rate is equal to the frequency nf.sub.o of the n.sup.th harmonic to be eliminated. The phase of this second pulse signal can be chosen so that its basic component is accurately in anti-phase with the harmonic to be eliminated in the first pulse signal. In a practical embodiment of this method each two-level pulse signal generated thus is applied to the control input of a corresponding switching circuit. Each switching circuit receives the signal x(t) via a signal input. The signals produced by the switching circuits are added in an adder device after having been multiplied by a predetermined weighting a first two-level pulse signal is generated having the pulse repetition rate f.sub.o and which does not contain the unwanted harmonics (let it, for example, be assumed that this pulse signal does not contain the even harmonics). If y(t) must now also be free from the odd n.sup.th harmonic (for example n=3), then a second two-level pulse signal is generated, whose pulse repetition rate is equal to the frequency nf.sub.o of the n.sup.th harmonic to be eliminated. The phase of this second pulse signal can be chosen so that its basic component is accurately in anti-phase with the harmonic to be eliminated in the first pulse signal. In a practical embodiment of this method each two-level pulse signal generated thus is applied to the control input of a corresponding switching circuit. Each switching circuit receives the signal x(t) via a signal input. The signals produced by the switching circuits are added in an adder device after having been multiplied by a predetermined weighting factor. The value of the weighting factor follows from expression (8) and is equal to 1/n.
With this method it is not only possible to generate with the aid of two-level pulse signals a multi-level signal y(t) in which the second and the third harmonics are absent, but a multi-level signal y(t) can even be obtained which in addition is free from the fourth and the fifth harmonics etc. In the last few years this property has appeared to be of considerable importance for stereo decoders, the reason being that it is increasingly tried to accommodate the complete stereo decoder on one IC and to avoid the use of a costly pre-modulation filter. As over the years the number of transmitters providing stereophonic wireless transmissions has increased very considerably, also the number of parasitic signals which may be converted to the AF-band has become increasingly larger. For example, in the expression (7) the quantity N may have the value seven, or even nine. By means of the last-described method it is indeed possible to avoid a simple premodulation filter having to be replaced again by a costly filter, but from Reference 2 it appears that a suitable implementation of this method for generating a multi-level signal y(t) which does not include a plurality of predetermined harmonics results in a very complicated and expensive circuit which for reasons of economy cannot be used in consumer equipment and which furthermore cannot be integrated on only one IC.